Which of the following numbers is a multiple of 2? ${63,67,109,113,120}$
Explanation: The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $63 \div 2 = 31\text{ R }1$ $67 \div 2 = 33\text{ R }1$ $109 \div 2 = 54\text{ R }1$ $113 \div 2 = 56\text{ R }1$ $120 \div 2 = 60$ The only answer choice that leaves no remainder after the division is $120$ $ 60$ $2$ $120$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $120$ $120 = 2\times2\times2\times3\times5 2 = 2$ Therefore the only multiple of $2$ out of our choices is $120$. We can say that $120$ is divisible by $2$.